**3.5 ****The first Ylemic Stars in the Universe **

The stability of stars is a function of the equilibrium condition, which balances the inward pull of gravity with the outward pressure of the thermodynamic energy or enthalpy of the star (H=PV+U). The Jeans Mass M_{J} and the Jeans Length R_{J} a used to describe the stability conditions for collapsing molecular hydrogen clouds to form stars say, are well known in the scientific data base, say in formulations such as:

M_{J}=3kTR/2Gm for a Jeans Length of: R_{J}=√{15kT/(4πρGm)}=R_{J} =√(kT/Gnm²).

Now the Ideal Gas Law of basic thermodynamics states that the internal pressure P and Volume of such an ideal gas are given by PV=nRT=NkT for n moles of substance being the Number N of molecules (say) divided by Avogadro's Constant L in n=N/L .

Since the Ideal Gas Constant R divided by Avogadro's Constant L and defines Boltzmann's Constant k=R/L. Now the statistical analysis of kinetic energy KE of particles in motion in a gas (say) gives a root-mean-square velocity (rms) and the familiar 2.KE=mv²(rms) from the distribution of individual velocities v in such a system.

It is found that PV=(2/3)N.KE as a total system described by the v(rms). Now set the KE equal to the Gravitational PE=GMm/R for a spherical gas cloud and you get the Jeans Mass. (3/2N).(NkT)=GMm/R with m the mass of a nucleon or Hydrogen atom and M=M_{J}=3kTR/2Gm as stated.

The Jeans' Length is the critical radius of a cloud (typically a cloud of interstellar dust) where thermal energy, which causes the cloud to expand, is counteracted by gravity, which causes the cloud to collapse. It is named after the British astronomer Sir James Jeans, who first derived the quantity; where k is Boltzmann Constant, T is the temperature of the cloud, r is the radius of the cloud, μ is the mass per particle in the cloud, G is the Gravitational Constant and ρ is the cloud's mass density (i.e. the cloud's mass divided by the cloud's volume).

Now following the Big Bang, there were of course no gas clouds in the early expanding universe and the Jeans formulations are not applicable to the mass seedling M_{o}; in the manner of the Jeans formulations as given.

However, the universe's dynamics is in the form of the expansion parameter of GR and so the R(n)=R_{max}(n/(n+1)) scalefactor of Quantum Relativity.

So we can certainly analyse this expansion in the form of the Jeans Radius of the first protostars, which so obey the equilibrium conditions and equations of state of the much later gas clouds, for which the Jeans formulations then apply on a say molecular level.

This analysis so defines the ylemic neutron stars as protostars and the first stars in the cosmogenesis and the universe.

Let the thermal internal energy or ITE=H be the outward pressure in equilibrium with the gravitational potential energy of GPE=Ω. The nuclear density in terms of the superbrane parameters is ρ_{critical}=m_{c}/V_{critical} with m_{c} a base-nuleon mass for a 'ylemic neutron'.

V_{critical}= 4πR_{e}^{3}/3 or the volume for the ylemic neutron as given by the classical electron radius

R_{e}=10^{10}λ_{wormhole}/360=e*/2c^{2}.

H=(molarity)kT for molar volume as N=(R/R_{e})^{3} for dH=3kTR^{2}/R_{e}^{3}.

Ω(R)= -∫G_{o}Mdm/R = -{3G_{o}m_{c}^{2}/(R_{e}^{3})^{2} }∫R^{4}dR = -3G_{o}m_{c}^{2}R^{5}/R_{e}^{6} for

dm/dR=d(ρV)/dR=4πρR^{2} and for ρ=3m_{c}/4πR_{e}^{3}

For equilibrium, the requirement is that dH=dΩ in the minimum condition dH+dΩ=0.

This gives: dH+dΩ=3kTR^{2}/R_{e}^{3} - 16G_{o}π^{2}ρ^{2}R^{4}/3=0 and the ylemic radius as:

**R _{ylem}=√{kTR_{e}/G_{o}m_{c}^{2}}**

as the Jeans-Length precursor or progenitor for subsequent stellar and galactic generation.

The ylemic (Jeans) radii are all independent of the mass of the star as a function of its nuclear generated temperature. Applied to the protostars of the vortex neutron matter or ylem, the radii are all neutron star radii and define a specific range of radii for the gravitational collapse of the electron degenerate matter.

This spans from the 'First Three Minutes' scenario of the cosmogenesis to 1.1 million seconds (or about 13 days) and encompasses the standard beta decay of the neutron (underpinning radioactivity). The upper limit defines a trillion degree temperature and a radius of over 40 km; the trivial Schwarzschild solution gives a typical ylem radius of so 7.4 kilometers and the lower limit defines the 'mysterious' planetesimal limit as 1.8 km.

For long a cosmological conundrum, it could not be modelled just how the molecular and electromagnetic forces applicable to conglomerate matter distributions (say gaseous hydrogen as cosmic dust) on the quantum scale of molecules could become strong enough to form say 1km mass concentrations, required for 'ordinary' gravity to assume control.

The ylem radii's lower limit is defined in this cosmology then show, that it is the ylemic temperature of the 1.2 billion degrees K, which perform the trick under the Ylem-Jeans formulation and which then is applied to the normal collapse of hydrogenic atoms in summation.

The stellar evolution from the ylemic (dineutronic) templates is well established in QR and confirms most of the Standard Model's ideas of nucleosynthesis and the general Temperature cosmology. The standard model is correct in the temperature assignment, but is amiss in the corresponding 'size-scales' for the cosmic expansion.

The Big Bang cosmogenesis describes the universe as a Planck-Black Body Radiator, which sets the Cosmic-Microwave-Black Body Background Radiation Spectrum (CMBBR) as a function of n as T^{4}=18.2(n+1)^{2}/n^{3} and derived from the Stefan-Boltzmann-Law and the related statistical frequency distributions.

We have the GR metric for Schwarzschild-Black Hole Evolution as R_{S}=2GM/c² as a function of the star's Black Hole's mass M and we have the ylemic Radius as a function of temperature only as R_{ylem}√(kT.R_{e}^{3}/G_{o}m_{c}^{2}).

The nucleonic mass-seed m_{c}=m_{P}.Alpha^{9} and the product G_{o}m_{c}^{2} is a constant in the partitioned n-evolution of

m_{c}(n)=Y^{n}.m_{c} and G(n)=G_{o}.X^{n}.

Identifying the ylemic Radius with the Schwarzschild Radius then indicates a specific mass a specific temperature and a specific radius.

Those we call the Chandrasekhar Parameters:

M_{Chandra}=1.5 solar Masses=3x10^{30} kg and R_{Chandra}=2G_{o}M_{Chandra}/c² or 7407.40704..metres, which is the typical neutron star radius inferred today.

T_{Chandra}=R_{Chandra}^{2}.G_{o}m_{c}^{2}/kR_{e}^{3} =1.985x10^{10} K for Electron Radius R_{e} and Boltzmann's Constant k.

Those Chandrasekhar parameters then define a typical neutron star with a uniform temperature of 20 billion K at the white dwarf limit of ordinary stellar nucleosynthetic evolution (Hertzsprung-Russell or HR-diagram).

The Radius for the massparametric Universe is given in R(n)=R_{max}(1-n/(n+1)) correlating the ylemic temperatures as the 'uniform' CMBBR-background and we can follow the evolution of the ylemic radius via the approximation:

R_{ylem}=0.05258..√T=(0.0753).[(n+1)^{2}/n^{3}]^{[1/8]}

R_{ylem}(n_{present}=1.1324..)=0.0868 m* for a T_{ylem}(n_{present} )=2.73 K for the present time

t_{present}=n_{present}/H_{o}.

What then is n_{Chandra}?

This would describe the size of the universe as the uniform temperature CMBBR today manifesting as the largest stars, mapped however onto the ylemic neutron star evolution as the protostars (say as n_{Chandra}'), defined not in manifested mass (say neutron conglomerations), but as a quark-strange plasma, (defined in QR as the Vortex-Potential-Energy or VPE).

R(n_{Chandra}')=R_{max}(n_{Chandra}'/(n_{Chandra}'+1))=7407.40741.. for n_{Chandra}'=4.64x10^{-23} and so a time of t_{Chandra}'=n_{Chandra}'/H_{o}=n_{Chandra}'/1.88x10^{-18}=2.47x10^{-5} seconds.

QR defines the Weyl-Temperature limit for Bosonic Unification as 1.9 nanoseconds at a temperature of 1.4x10^{20} Kelvin and the weak-electromagnetic unification at 1/365 seconds at T=3.4x10^{15} K.

So we place the first ylemic protostar after the bosonic unification (before which the plenum was defined as undifferentiated 'bosonic plasma'), but before the electro-weak unification, which defined the Higgs-Bosonic restmass induction via the weak interaction vector-bosons and allowing the dineutrons to be born.

The universe was so 15 km across, when its ylemic 'concentrated' VPE-Temperature was so 20 Billion K and we find the CMBBR in the Stefan-Boltzmann-Law as:

T^{4}=18.20(n+1)^{2}/n^{3}=1.16x10^{17} Kelvin.

So the thermodynamic temperature for the expanding universe was so 5.85 Million times greater than the ylemic VPE-Temperature; and implying that no individual ylem stars could yet form from the mass seedling M_{o}.

The universe's expansion however cooled the CMBBR background and we to calculate the scale of the universe corresponding to this ylemic scenario; we simply calculate the 'size' for the universe at T_{Chandra}=20 Billion K for T_{Chandra}^{4} and we then find n_{Chandra}=4.89x10^{-14} and t_{Chandra}=26,065 seconds or so 7.24 hours.

The Radius R(n_{Chandra})=7.81x10^{12} metres or 7.24 lighthours.

This is about 52 Astronomical Units and an indicator for the largest possible star in terms of radial extent and the 'size' of a typical solar system, encompassed by supergiants on the HR-diagram.

We so know that the ylemic temperature decreases in direct proportion to the square of the ylemic radius and one hitherto enigmatic aspect in cosmology relates to this in the planetesimal limit. Briefly, a temperature of so 1.2 billion degrees defines an ylemic radius of 1.8 km as the dineutronic limit for proto-neutron stars contracting from so 80 km down to this size just 1.1 million seconds or so 13 days after the Big Bang.

This then 'explains' why chunks of matter can conglomerate via molecular and other adhesive interactions towards this size, where then the accepted gravity is strong enough to build planets and moons. It works, because the ylemic template is defined in subatomic parameters reflecting the mesonic-inner and leptonic outer ring boundaries, the planetesimal limit being the leptonic mapping. So neutrino- and quark blueprints micromacro dance their basic definition as the holographic projections of the spacetime quanta.

Now because the Electron Radius is directly proportional to the linearised wormhole perimeter and then the Compton Radius via Alpha in R_{e}=10^{10}λ_{wormhole}/360=e*/2c^{2}=Alpha.R_{Compton}, the Chandrasekhar White Dwarf limit should be doubled to reflect the protonic diameter mirrored in the classical electron radius.

Hence any star experiencing electron degeneracy is actually becoming *ylemic* or *dineutronic*, the boundary for this process being the Chandrasekhar mass. This represents the subatomic mapping of the first Bohr orbit collapsing onto the leptonic outer ring in the quarkian wave-geometry.

But this represents the Electron Radius as a Protonic Diameter and the Protonic Radius must then indicate the limit for the scale where proton degeneracy would have to enter the scenario. As the proton cannot degenerate in that way, the neutron star must enter Black Hole phasetransition at the R_{e}/2 scale, corresponding to a mass of 8M_{Chandra}=24x10^{30} kg* or 12 solar masses.

The maximum ylemic radius so is found from the constant density proportion ρ=M/V:

(R_{ylemmax}/R_{e})^{3}=M_{Chandra}/m_{c} for R_{ylemmax}=40.1635 km.

The corresponding ylemic temperature is 583.5 Billion K for a CMBBR-time of 287 seconds or so 4.8 minutes from a n=5.4x10^{-16}, when the universe had a diameter of so 173 Million km.

But for a maximum nuclear compressibility for the protonic radius, we find:

(R_{ylemmax}/R_{e})^{3}=8M_{Chandra}/m_{c} for R_{ylemmax}=80.327 km, a ylemic temperature of 2,334 Billion K for a n-cycletime of 8.5x10^{-17} and a CMBBR-time of so 45 seconds and when the universe had a radius of 13.6 Million km or was so 27 Million km across.

The first ylemic protostar vortex was at that time manifested as the ancestor for all neutron star generations to follow. This vortex is described in a cosmic string encircling a spherical region so 160 km across and within a greater universe of diameter 27 Million km which carried a thermodynamic temperature of so 2.33 Trillion Kelvin at that point in the cosmogenesis.

This vortex manifested as a VPE concentration after the expanding universe had cooled to allow the universe to become transparent from its hitherto defining state of opaqueness and a time known as the decoupling of matter (in the form of the M_{o} seedling partitioned in m_{c}'s) from the radiation pressure of the CMBBR photons.

The temperature for the decoupling is found in the galactic scale-limit modular dual to the wormhole geodesic as 1/λ_{wormhole}=λ_{antiwormhole}=λ_{galaxyserpent}=10^{22} metres or so 1.06 Million ly and its luminosity attenuation in the 1/e proportionality for then 388,879 lightyears as a decoupling time n_{decoupling}.

A maximum galactic halo limit is modulated in 2πλ_{antiwormhole} metres in the linearisation of the Planck-length encountered before in an earlier discussion.

R(n_{decoupling})=R_{max}(n_{decoupling}/(n_{decoupling}c+1))=10^{22} metres for n_{decoupling}=6.26x10^{-5} and so for a CMBBR-Temperature of about T=2935 K for a galactic protocore then attenuated in so 37% for n_{decouplingmin}=1.0x10^{-6} for R=λ_{antiwormhole}/2π and n_{decouplingmax}=3.9x10^{-4} for R=2πλ_{antiwormhole} and for temperatures of so 65,316 K and 744 K respectively, descriptive of the temperature modulations between the galactic cores and the galactic halos.

So a CMBBR-temperature of so 65,316 K at a time of so 532 Billion seconds or 17,000 years defined the initialisation of the VPE and the birth of the first ylemic protostars as a decoupling minimum. The ylemic mass currents were purely monopolic and known as superconductive cosmic strings, consisting of nucleonic neutrons, each of mass m_{c}.

If we assign this timeframe to the maximised ylemic radius and assign our planetesimal limit of fusion temperature 1.2 Billion K as a corresponding minimum; then this planetesimal limit representing the onset of stellar fusion in a characteristic temperature, should indicate the first protostars at a temperature of the CMBBR of about 744 Kelvin.

The universe had a tremperature of 744 K for n_{decouplingmax}=3.9x10^{-4} for R=2πλ_{antiwormhole} and this brings us to a curvature radius of so 6.6 Million lightyears and an 'ignition-time' for the first physical ylemic neutron stars as first generation protostars of so 7 Million years after the Big Bang.

The important cosmological consideration is that of distance-scale modulation.

The Black Hole Schwarzschild metric is the inverse of the galactic scale metric.

The linearisation of the Planck-String as the Weyl-Geodesic and so the wormhole radius in the curvature radius R(n) is modular dual and mirrored in inversion in the manifestation of galactic structure with a nonluminous halo a luminous attenuated diameter-bulge and a superluminous (quasar or White Hole Core).

The core-bulge ratio will so reflect the eigenenergy quantum of the wormhole as heterotic Planck-Boson-String or as the magnetocharge as 1/500, being the mapping of the Planck-Length-Bounce as e=l_{P}.c²√Alpha onto the electron radius in e*=2R_{e}.c².